#Javascript - 206 Bytes#

r=>{var a="lucky";r:for(var e=5;e>0;e--)for(var n=0;6>n+e;n++){var o=a.substring(n,e+n);if(r.includes(o))break r}for(var t=0,e=0;e<r.length;e++)('omen'.indexOf(r[e])+1)&&t++;return Math.pow(2,o.length)-2*t}

Javascript - 206 Bytes

r=>{var a="lucky";r:for(var e=5;e>0;e--)for(var n=0;6>n+e;n++){var o=a.substring(n,e+n);if(r.includes(o))break r}for(var t=0,e=0;e<r.length;e++)('omen'.indexOf(r[e])+1)&&t++;return Math.pow(2,o.length)-2*t}

#Javascript - 237 Bytes#

function luck(r){r=r.toLowerCase();var a="lucky";r:for(var e=5;e>0;e--)for(var n=0;6>n+e;n++){var o=a.substring(n,e+n);if(r.includes(o))break r}for(var t=0,e=0;e<r.length;e++)('omen'.indexOf(r[e])+1)&&t++;return Math.pow(2,o.length)-2*t}

#Javascript - 206 Bytes#

r=>{var a="lucky";r:for(var e=5;e>0;e--)for(var n=0;6>n+e;n++){var o=a.substring(n,e+n);if(r.includes(o))break r}for(var t=0,e=0;e<r.length;e++)('omen'.indexOf(r[e])+1)&&t++;return Math.pow(2,o.length)-2*t}

#Javascript - 257 Bytes#

function luck(r){r=r.toLowerCase();var a="lucky";r:for(var e=5;e>0;e--)for(var n=0;6>n+e;n++){var o=a.substring(n,e+n);if(r.includes(o))break r}for(var t=0,e=0;e<r.length;e++)("o"==r[e]||"m"==r[e]||"e"==r[e]||"n"==r[e])&&t++;return Math.pow(2,o.length)-2*t}

#Javascript - 237 Bytes#

function luck(r){r=r.toLowerCase();var a="lucky";r:for(var e=5;e>0;e--)for(var n=0;6>n+e;n++){var o=a.substring(n,e+n);if(r.includes(o))break r}for(var t=0,e=0;e<r.length;e++)('omen'.indexOf(r[e])+1)&&t++;return Math.pow(2,o.length)-2*t}